Chapter I: Front Matter

GROWTH AND FORM

CAMBRIDGE UNIVERSITY PRESS

C. F. CLAY, MANAGER

London: FETTER LANE, E.C.

Edinburgh: 100 PRINCES STREET

New York: G. P. PUTNAM’S SONS

Bombay, Calcutta and Madras: MACMILLAN AND Co., LTD.

Toronto: J. M. DENT AND SONS, LTD.

Tokyo: THE MARUZEN-KABUSHIKI-KAISHA

_All rights reserved_

ON GROWTH AND FORM

BY

D’ARCY WENTWORTH THOMPSON

Cambridge: at the University Press 1917

“The reasonings about the wonderful and intricate operations of nature are so full of uncertainty, that, as the Wise-man truly observes, _hardly do we guess aright at the things that are upon earth, and with labour do we find the things that are before us_.” Stephen Hales, _Vegetable Staticks_ (1727), p. 318, 1738.

PREFATORY NOTE

This book of mine has little need of preface, for indeed it is “all preface” from beginning to end. I have written it as an easy introduction to the study of organic Form, by methods which are the common-places of physical science, which are by no means novel in their application to natural history, but which nevertheless naturalists are little accustomed to employ.

It is not the biologist with an inkling of mathematics, but the skilled and learned mathematician who must ultimately deal with such problems as are merely sketched and adumbrated here. I pretend to no mathematical skill, but I have made what use I could of what tools I had; I have dealt with simple cases, and the mathematical methods which I have introduced are of the easiest and simplest kind. Elementary as they are, my book has not been written without the help—the indispensable help—of many friends. Like Mr Pope translating Homer, when I felt myself deficient I sought assistance! And the experience which Johnson attributed to Pope has been mine also, that men of learning did not refuse to help me.

My debts are many, and I will not try to proclaim them all: but I beg to record my particular obligations to Professor Claxton Fidler, Sir George Greenhill, Sir Joseph Larmor, and Professor A. McKenzie; to a much younger but very helpful friend, Mr John Marshall, Scholar of Trinity; lastly, and (if I may say so) most of all, to my colleague Professor William Peddie, whose advice has made many useful additions to my book and whose criticism has spared me many a fault and blunder.

I am under obligations also to the authors and publishers of many books from which illustrations have been borrowed, and especially to the following:―

To the Controller of H.M. Stationery Office, for leave to reproduce a number of figures, chiefly of Foraminifera and of Radiolaria, from the Reports of the Challenger Expedition. {vi}

To the Council of the Royal Society of Edinburgh, and to that of the Zoological Society of London:—the former for letting me reprint from their _Transactions_ the greater part of the text and illustrations of my concluding chapter, the latter for the use of a number of figures for my chapter on Horns.

To Professor E. B. Wilson, for his well-known and all but indispensable figures of the cell (figs. 42–51, 53); to M. A. Prenant, for other figures (41, 48) in the same chapter; to Sir Donald MacAlister and Mr Edwin Arnold for certain figures (335–7), and to Sir Edward Schäfer and Messrs Longmans for another (334), illustrating the minute trabecular structure of bone. To Mr Gerhard Heilmann, of Copenhagen, for his beautiful diagrams (figs. 388–93, 401, 402) included in my last chapter. To Professor Claxton Fidler and to Messrs Griffin, for letting me use, with more or less modification or simplification, a number of illustrations (figs. 339–346) from Professor Fidler’s _Textbook of Bridge Construction_. To Messrs Blackwood and Sons, for several cuts (figs. 127–9, 131, 173) from Professor Alleyne Nicholson’s _Palaeontology_; to Mr Heinemann, for certain figures (57, 122, 123, 205) from Dr Stéphane Leduc’s _Mechanism of Life_; to Mr A. M. Worthington and to Messrs Longmans, for figures (71, 75) from _A Study of Splashes_, and to Mr C. R. Darling and to Messrs E. and S. Spon for those (fig. 85) from Mr Darling’s _Liquid Drops and Globules_. To Messrs Macmillan and Co. for two figures (304, 305) from Zittel’s _Palaeontology_, to the Oxford University Press for a diagram (fig. 28) from Mr J. W. Jenkinson’s _Experimental Embryology_; and to the Cambridge University Press for a number of figures from Professor Henry Woods’s _Invertebrate Palaeontology_, for one (fig. 210) from Dr Willey’s _Zoological Results_, and for another (fig. 321) from “Thomson and Tait.”

Many more, and by much the greater part of my diagrams, I owe to the untiring help of Dr Doris L. Mackinnon, D.Sc., and of Miss Helen Ogilvie, M.A., B.Sc., of this College.

D’ARCY WENTWORTH THOMPSON.

UNIVERSITY COLLEGE, DUNDEE.

_December, 1916._

CONTENTS

CHAP. PAGE
I. INTRODUCTORY 1

II. ON MAGNITUDE 16

III. THE RATE OF GROWTH 50

IV. ON THE INTERNAL FORM AND STRUCTURE OF THE CELL 156

V. THE FORMS OF CELLS 201

VI. A NOTE ON ADSORPTION 277

VII. THE FORMS OF TISSUES, OR CELL-AGGREGATES 293

VIII. THE SAME (_continued_) 346

IX. ON CONCRETIONS, SPICULES, AND SPICULAR SKELETONS 411

X. A PARENTHETIC NOTE ON GEODETICS 488

XI. THE LOGARITHMIC SPIRAL 493

XII. THE SPIRAL SHELLS OF THE FORAMINIFERA 587

XIII. THE SHAPES OF HORNS, AND OF TEETH OR TUSKS: WITH
A NOTE ON TORSION 612

XIV. ON LEAF-ARRANGEMENT, OR PHYLLOTAXIS 635

XV. ON THE SHAPES OF EGGS, AND OF CERTAIN OTHER HOLLOW
STRUCTURES 652

XVI. ON FORM AND MECHANICAL EFFICIENCY 670

XVII. ON THE THEORY OF TRANSFORMATIONS, OR THE COMPARISON
OF RELATED FORMS 719